Justify why 22 - 7 is rational but - is irrational

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Standard IX

Mathematics

Natural Numbers

Justify why 2...

Question

Justify why 22/7 is rational but π is irrational

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Solution

Irrational numbers can't be represented as a fraction with integers as the numerator and denominator. 227227 is a fraction with integers as it's numerator and denominator. Therefore, 227227 is not irrational.

227227 is often used as an approximation for ππ. However, 227227 does not equal ππ. 227≈3.1428571429227≈3.1428571429, while π≈3.1415926536π≈3.1415926536.

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